How can a body transition between soft and rigid during animation?
As LukeD's comment suggested, you can animate the soft body stiffness.

I you want to key the rigid part yourself, use the soft body goal and animate its stiffness value.



Resulting in a transition between manually keyed animation and soft body simulation.



You can also animate the push and pull for the Soft Body Edges. Here, I animated them from low values (0.2, 0.4) to 0.999.



As you can see, in them second example, the object's origin stays motionless as it has no animation.